The Ibn Ezra writes that Haman pushed his way home.
M’nos HaLevi explains that this detail needed to be said here because his pushing his way forward was unique for Haman since he usually had servants to do it for him, but not on this tragically embarrassing night.
The Vilna Gaon says he ran because he was embarrassed.
R’ Yitzchak Eliyahu Landau writes that Haman was pushed away by others because he smelled from his daughter’s chamber pot.
The Steipler Gaon writes that the king’s guards pushed Haman because thet were concerned that he was coming to speak with Achashverosh in his current, dirty state.
M’nos HaLevi and Dena Pishra write that Haman had to push through the crowd, which was unique for him since people used to push to see him.
M’nos HaLevi also cites a verse in Divrei HaYamim 2 (26:20) that Uziya pushed through people because he suffered from tzaras on his last days, and was embarrassed to be found that way. Similarly, Haman was embarrassed by his disgusting situation at the end of his own reign.
In R’ Dovid Feinstein’s view, this important day started out with Haman wanting to persuade Achashverosh to kill Mordechai, but the events of the day pushed/forced Haman to go home, instead.
The Ben Ish Chai explains that the word nidchaf (“was propelled”) can mean nad (“eulogy”) and yachaf (“barefoot”) indicating the Talmud’s (Megillah 16a) opinion that he was in mourning for his daughter. It can also indicate nad (“moved”) pach (“trap”), emphasizing that Haman’s trap for Mordechai had been moved from his jurisdiction.
R’ Moshe Dovid Valle shows that Haman’s own harsh decrees pushed him. He writes, “nafal sora chadad l’sechina,” or the sharp bull fell on a knife. H-Shem’s supervision of the world allows justice to triumph in the end. As the prophet tells us (Yirmiya 17:11), “oseh osher v’lo b’mishpat, b’chatzi yamav yi’azvenu, u’bi’achariso yih’ye naval,” or one who becomes wealthy unjustly will lose it in the course of one’s days, and in one’s end will be a fool. Haman’s wealth, too, came to him with lying about not being a slave, and his current appearance indeed makes him seem foolish.